Given the thinness of the upper liquid film, one may wonder in which conditions intermolecular long-range forces would be expected to have a noticeable effect on the upper film dynamics.
These interactions in the film are usually quantified by the disjoining pressure isotherm [1]}, which measures the relative force acting between its two interfaces as a function of their separation.
For asymmetric films made of a pure liquid, such as our upper film of liquid 2, the disjoining pressure isotherm only contains van der Waals interactions, whose nature (attractive or repulsive) depends on the sign of the Hamaker constant \(A\)  [2]}.
Following the approach of [3]}, the effect of van der Waals interactions can be included in our formulation by adding a disjoining pressure gradient \(\hat{\Pi }^{\rm d}\)  to the capillary pressure gradients \(\hat{\Pi }_1\)  and \(\hat{\Pi }_2\)  defined in Appendix .
Considering only non-retarded van der Waals forces [4]} and using the rescaling exposed in § REF  and § REF , the disjoining pressure gradient reads
\(\hat{\Pi }^{\rm d} = Ca^{-2} \mathcal {A} \frac{\hat{h}^{\prime }_2 - \hat{h}^{\prime }_1}{(\hat{h}_2-\hat{h}_1)^4},\) 
